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# Probabilities

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1. This problem is in reference to students who may or may not take advantage of the opportunities provided in QMB such as homework. Some of the students pass the course, and some of them do not pass. Research indicates that 40% of the students do the assigned homework. Of the students who do homework, there is an 80% chance they will pass the course. The probability of not passing if the students does not do the homework is 90%. What is the probability of a student not doing homework or passing?

2. In a survey about soft drinks it was found that 5% of the respondents like diet soft drinks. 12% of the respondents like the brand Coke. Of the diet soda drinkers, 40% like Coke. What is the probability that a respondent did like diet drinks or did not like Coke?

https://brainmass.com/math/probability/probabilities-444571

#### Solution Preview

1. Probabilities given:
Candidates doing home work P(H) = 0.4
Candidates not doing homework P(NH) = 1.0 - 0.4 = 0.6

Candidates passed from group of doing home work P(P/H) = 0.8
Candidates not passed from group of not doing homework P(NP/NH) = 0.9

Calculations:
Probability of candidates passed who did assignment P(P AND H) = P(H) * P(P/H) = 0.4*0.8 = ...

#### Solution Summary

Probabilities are reiterated clearly.

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